The DIP approach, as well as our extension to the dynamic setting in (REF ), is vulnerable to noise overfitting. In particular, if the generator networks have sufficient capacity, it will learn the noise in the measurements when the number of iterations is large [1]}. To further improve the robustness of the algorithm to noise, we propose to additionally penalize the \(\ell _1\)  norm of the network weights. The regularized recovery is posed as
\(\nonumber \lbrace \mathbf {U}^*,\mathbf {V}^*\rbrace  &=& \min _{\theta ,\phi ,\mathbf {Z}} \left\Vert \mathcal {A}(\mathbf {U}\mathbf {V}^T) -\mathbf {B}\right\Vert ^2\\\nonumber &&\qquad + \underbrace{\lambda _1 \Vert \theta \Vert _{\ell _1} + \lambda _2 \Vert \phi \Vert _{\ell _1}}_{\mbox{\scriptsize network regularization}} + \underbrace{\lambda _3 \Vert \nabla _t \mathbf {Z}\Vert _{\ell _1}}_{\mbox{\scriptsize temporal regularization}},\\\nonumber \\\nonumber &&\qquad \mbox{ such that } \mathbf {U} = \mathcal {G}_{\theta }\left[\mathbf {U}_0\right]; \mathbf {V} = \mathcal {G}_{\phi }\left[\mathbf {Z}\right]\\\) 
